How can I model these support wires?
Go to File &gt; User Preferences &gt; Addons and search for Add Curve: Extra Objects and activate this addon
In the 3D view add a new curve object from the Spiral type. Adjust its settings as desired.
Add a new curve circle with a radius similar to the sphere.
Now to the spiral curve apply an Array modifier fit to a curve using the circle as length definition.
Next add a curve modifier to it using again the circle as deformation curve.

You can now freely adjust the bezier curve circle as desired to match desired length and radius. Set it's handles to Free and then subdivide it to make shorter segments.

EDIT
The trick here is using a bezier circle as deformation in the Curve modifier, since it will guarantee a perfect fit around the sphere as long as the body is truly spherical. You can then rotate both objects at the same time (curve circle and spring-like spiral) at will and it should always fit around the curve.